Similar equations hold for r(r t) and H CF(r t). In this way the single partial differential equation in R and r is split into two ordinary differential equations, one for each degree of freedom. [Pg.88]

Several improvements of the TDSCF approach have been proposed in the recent literature (Kucar, Meyer, and Cederbaum 1987 Makri and Miller 1987 Meyer, Kucar, and Cederbaum 1988 Kotler, Nitzan, and Kosloff 1988 Meyer, Manthe, and Cederbaum 1990 Campos-Martinez and Coalson 1990 Waldeck, Campos-Martinez, and Coalson 1991). [Pg.89]

In both the time-dependent and time-independent SCF perturbation theories the equations determining the effect of the perturbation look as if they can generate a finite effect with no applied perturbation. These cases of infinitesimal perturbations" are genuine ones which have important ramifications for the stabilities of the single-determinant states of a many-electron system. [Pg.711]

The field- and time-dependent cluster operator is defined as T t, ) = nd HF) is the SCF wavefunction of the unperturbed molecule. By keeping the Hartree-Fock reference fixed in the presence of the external perturbation, a two step approach, which would introduce into the coupled cluster wavefunction an artificial pole structure form the response of the Hartree Fock orbitals, is circumvented. The quasienergy W and the time-dependent coupled cluster equations are determined by projecting the time-dependent Schrodinger equation onto the Hartree-Fock reference and onto the bra states (HF f[[exp(—T) [Pg.115]

The equations to be solved for the time-dependent SCF first-order perturbation correction" are, in the absence of a perturbation [Pg.329]

Olsen, J., lorgcnsen, P. Time dependent response theory with appUcations in to self consistence field (SCF and multiconfigurational self consistent field (MCSCF) wave functions, l.F.A. PRINT, Aarhus Universitet, 1994 [Pg.249]

Enthalpy changes may be obtained with units (English) of Btu, Btu/lb, Btu/lbmol, Btu/scf, or Btu/time depending on the available data and calculation required. [Pg.29]

There are no new requirements for the implementation of the time-independent or time-dependent SCF equations except the generation of the electron-repulsion integrals over the molecular orbitals. We now turn to this integral transformation problem. [Pg.714]

The clue lies in the idea of the transitions of the analogous time-dependent case there are solutions of the ordinary time-independent SCF equations which are unstable or metastable in the following senses [Pg.331]

Calculated CD curve for each conformer by De Voe coupled oscillator, 7r-electron SCF-CI-DV MO, time-dependent DFT (TDDFT) [Pg.99]

An approximation which is convergent to the exact solution of the time-dependent Schrddinger equation can be generated with the multi configuration time dependent SCF scheme. Therein the summation in eq. (3) is truncated to a finite number N [Pg.131]

The SCF, or mean-field, approximation does not include the effect of energy transfer processes between the modes. The Cl approach incorporates such effects in a time-independent framework, but as was noted in the previous section this method loses much of the simplicity and insight provided by the SCF model. The most natural extension of the SCF approximation that also describes energy transfer among the coupled modes in the system, and treats this effect by a mean-field approach, is the time-dependent self-consistent-field (TDSCF), or time-dependent mean-field, approximation. [Pg.117]

While the (one-particle) Brillouin condition BCi has been known for a long time, and has played a central role in Hartree-Fock theory and in MC-SCF theory, the generalizations for higher particle rank were only proposed in 1979 [38], although a time-dependent formulation by Thouless [39] from 1961 can be regarded as a precursor. [Pg.318]

The central assumption behind the derivations in this chapter has been that the frequency of the time-dependent perturbation was such that the system responded to the perturbation by vibrating with that frequency. Consideration of the effect of perturbations for which this assumption is not true will lead to a much more convenient form for the time-dependent SCF perturbation expressions, which eliminates the need to solve separate equations at each frequency and, more surprisingly, for each separate spatial form of the perturbation /. [Pg.326]

For the case of intramolecular energy transfer from excited vibrational states, a mixed quantum-classical treatment was given by Gerber et al. already in 1982 [101]. These authors used a time-dependent self-consistent field (TDSCF) approximation. In the classical limit of TDSCF averages over wave functions are replaced by averages over bundles of trajectories, each obtained by SCF methods. [Pg.16]

UV spectra usually involve electronic state transitions, so that simple Hartree-Fock and DFT calculations often are not sufficient PCM has been recently extended also to multi-configurational (MC-SCF) calculations [113] and to time-dependent approaches, allowing for the description of excited states and then the prediction of the so-called solvatochromic effects on these spectra. Nuclear magnetic resonance (NMR) and electron spin resonance (EPR) spectra are even more influenced by solute-solvent interactions moreover, the interpretation of experimental data is often very difficult without the support of reliable ab initio calculation, especially for EPR which is usually applied to unstable radical species. [Pg.507]

We will restrict the further considerations to the case, where only one product in the expansion of the total wave function is relevant. Instead of the MCTDSCF approximation the solution is approximated by a single product function wherein these functions are determined in a self consistent way (time dependent SCF approximation, TDSCF). The situation is similar to that where there are several electronic degrees of freedom for a molecule, but where it has been demonstrated that the a batic Bom-Oppenheimer approximation works substantially well for the description of most spectroscopic and other properties of molecules. [Pg.132]

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